First I would double fist pump that I proved all those people wrong who said knowing three dead languages would never help me in a practical way.
I suppose that gives me a huge leg up. I'd pretend to be mute for awhile (selling watch and clothes to provide for basic needs for a few years). It'd take some time to get conversational at ancient Greek and Latin (we have no idea how they were pronounced and I'm a bit rusty). But then it'd be easy to convince people I was an educated man from a foreign land to the east (Rome was a cosmopolitan city, and I wouldn't be the first person with a very strange accent). As a writer and speaker of two languages, I would easily be in the top 1% of people and in the top .001% of free people. Some house would take me in as a house philosopher (yeah, what nerds, right?). Then, with some assurance that my crazy ideas wouldn't be taken for witchcraft and have me burned at the stake, I could start getting all sciency. This is where'd I'd suck a lot compared to many. But things would, no doubt, occur to me.

/all assumes I don't immediately get identified as a runaway slave

Also, it wouldn't be the worst thing to be a slave in a rich house. Educated slaves in palaces had far better lives than the majority of free people. If you could manage to convince people you weren't a witch, then your novelty as a freakishly tall (average height 5'6") big person would probably get some house to want to indenture you to them.

actually I was thinking you're gonna need to suck a lot of dick before you become the house philosopher. You first need to be an understudy, and back then the nerdy thing to do was to pleasure your philosopher master as you may know.

i think i'd try to become a stand up philosopher instead.

Gunpowder: All you need is sulphur, charcoal and potassium nitrate (which can be obtained from piss).

Disclaimer: I know the basics but it would probably take me years to make it work

A big thing that no one mentioned is Arabic numbers. Accounting and the like in Roman Numerals sucked balls. If you were able to get an businessman to spend 20 minutes with you, you'd be set.

It is a little more involved than that. I don't know the actual process but to get potassium nitrate the way you are thinking involves ****, rotting biomass (not sure if the composition is important but I think hay and wood was used) and then urine. I guess there is a limited number of ways to combine this so over time you'd get there but I think going for a way to get a current and then using that to get hydrogen would likely be easier.

I think it's easier than that, it took Captain Kirk like 20 minutes.